Reinforcing Assemblies and Reinforced Concrete Structures

ABSTRACT

Reinforcing assemblies for use in structural concrete members, as well as reinforced concrete structures, are provided that are uniquely suited to deal with punching shear failure in structural concrete members such as slabs, beams footings and flat foundations. The reinforcing assemblies include a support base, comprising two elongate rebar members disposed substantially parallel to each other, and several shear-resisting rebar elements having two opposing ends and cast, or bent, in hairpin shape on a common plane in generally parallel orientation to each other and secured to the base. The reinforced concrete structures include a concrete member, having a first face and a generally opposed second face, and at least four reinforcing assemblies that are embedded and retained at prescribed locations within the concrete member by their base and by the opposed faces of the concrete member, and which comprise a support base and multiple hairpin-shaped rebar elements secured to the support base.

FIELD OF THE INVENTION

This invention relates to reinforcing assemblies for use in structural concrete members. In particular, this invention is concerned with a reinforcing system that is uniquely suited to deal with shear failure and with punching shear failure in structural concrete members such as slabs, beams, footings and flat foundations. More particularly, the invention relates to a structural concrete reinforcing assembly that may be made entirely of rebar. Specifically, the invention relates to a novel technique for eliminating or minimizing shear failure and punching shear failure in structural concrete members such as slabs, beams, footings and flat foundations by means of a unique reinforcing assembly made up of hairpin-shaped rebars, which novel technique allows the user to fabricate reinforced concrete structures with enhanced punching-shear-resistant capabilities.

BACKGROUND OF THE INVENTION

Commercial concrete is a mixture of cement, sand and stone aggregate held together as rigid structures by the action of small amounts of water. While concrete made in this fashion, usually referred to as “unreinforced concrete”, has fairly good resistance to compressive stresses, any significant tension will tend to break the rigid structure and cause undesirable cracking and separation of the concrete. For practical reasons, most commercial and industrial structural concrete members are made of “reinforced concrete”, that is, from a mixture of cement, sand and stone aggregate where a solid member made of a material with high strength in tension, such as steel, is placed and made to remain embedded. Reinforced concrete sections where the concrete is capable of resisting the compression and the steel placed inside is designed to resist the tension are often made into many shapes and sizes for the construction industry. Commercial and industrial structural concrete members such as slabs, beams, footings and flat foundations, even when made with reinforced concrete, are susceptible to shear forces that create tensile forces along them and often result in structural failure, that is, undesirable cracking and/or breaking of the structural concrete members. The type of failure caused by these shear forces and the attendant incline cracks that tend to propagate throughout the concrete, usually from the area under tension towards the area under compression, are not always easy to detect and correct since they are often not visible when they occur. One-way shear failure, often referred to as “shear failure”, usually occurs in beams and, occasionally, in walls, slabs, footings and other vertical members. Two-way shear failure, often referred to as “punching shear failure”, tends to occur in horizontal concrete members such as slabs, footings and flat foundations. Various methods and techniques exist for reinforcing structural concrete members so as to prevent or minimize the undesirable cracking and/or breaking of concrete structures caused by shear forces. Some of the methods and techniques that are commonly employed with various degrees of success include the use of open or closed stirrups that are strategically placed in designated areas of the concrete structures. A particular type of situation that is often encountered, for example when a load-bearing concrete slab is supported by a column, is what is commonly referred to as “punching shear” failure. Shear strength of flat slabs in the vicinity of columns or concentrated loads is often controlled by the two-way shear known as “punching shear”. Shear considerations can therefore be the controlling factor in determining the required slab thickness or increasing column size, especially of post-tensioned (“PT”) flat-plates. Punching shear failure is usually a substantial inclined cracking that occurs at about a 19-to-34-degree angle with respect to the top surface of a PT slab and extends from the edge of the load being applied. Post-tensioned slabs and slabs that make use of high-strength concrete are particularly susceptible to punching shear failure. Conventional solutions to shear problems are not always satisfactory when dealing with punching shear problems. To prevent punching shear failure at slab-column connections, conventional solutions usually provide for the use of stirrups, structural steel shearheads or studrail reinforcements. Each of these techniques, while adequate in many cases, also has its share of disadvantages.

Stirrups, with longitudinal bars or with vertical bars, are difficult to place in the concrete structures and often present anchorage slip problems. Increasing the strength of concrete slabs with conventional stirrups is common, but the anchorage of stirrups is difficult to provide in thin slabs (e.g., less than about 6 inches in height) and therefore should be used only if the stirrups are closed and contain a longitudinal bar at each corner. The use of the stirrups as shear reinforcements in slabs is practicable only if the effective depth of the slab is greater than about 6 inches, but not less than 16 times the shear reinforcement bar diameter. So-called “shearheads” are structural steel shapes such as “I” shapes or channel sections. Shearheads are rarely used because their installation is very expensive and because they often interfere with the placement of flexural reinforcing bars and post-tensioned cables. So-called “studrails” consist of headed studs in the form of vertical bars mechanically anchored at each end by a plate or head capable of developing the yield strength of the bars. Studrails are often used to increase the shear strength in flat slabs, but in order to develop the full yield strength of the studs the area of the anchor head must be a minimum of 10 times the cross sectional area of the stud stem. Also, because of their anchor heads, studrails do not always provide adequate confinement of the concrete where the punching shear failure tends to occur.

It is apparent that a need exists to provide a solution to the problems associated with punching shear failure that does not suffer from the shortcomings attendant the use of stirrups, shearheads, studrails and similar conventional devices currently in commercial use. The present invention provides one such solution.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a practicable and economical solution to the problems associated with shear failure and punching shear failure in concrete structures. Another object of the present invention is to provide a safe and cost-effective reinforcing assembly for use in structural concrete members that is uniquely suited to deal with shear failure and punching shear failure in structural concrete members such as slabs, beams, footings and flat foundations. It is also an object of this invention to provide a structural concrete reinforcing assembly that may be made entirely of rebar members. An additional object of the invention is to provide a safe and low-cost reinforced concrete structure that is particularly resistant to punching shear forces and that is uniquely suited for commercial use with structural concrete members such as slabs, footings and flat foundations. A further object of the invention is to provide a structural concrete reinforcing assembly that is particularly effective at eliminating or minimizing shear failure in structural concrete members while affording better anchorage than the conventional devices used in preventing or minimizing shear failures. A particular object of the invention is to facilitate an efficient technique for eliminating or minimizing shear failure in structural concrete members such as slabs, footings and flat foundations by means of a unique reinforcing assembly that may be made up entirely of hairpin-shaped rebars, which novel technique permits the fabrication of reinforced concrete structures with enhanced punching-shear-resistant capabilities. These and other objects of the invention will be apparent from the disclosures that follow.

The reinforcing assembly of the present invention involves a support base that comprises two elongate rebar members disposed substantially parallel to each other, and several shear-resisting rebar elements having two opposing ends and a hairpin shape on a common plane in generally parallel orientation to each other and secured to the base. The rebar elements may be cast in the hairpin shape, or they may be reformed by bending; and they may have a smooth surface, which affords cost savings, or be ribbed or corrugated in order to improve cohesion between the steel and the concrete. The reinforcing assemblies of the present invention are best used as sets of four units that are strategically placed at or near the areas of high shear failure propensity. The reinforced concrete structure of the invention includes a concrete member, having a first face and a generally opposed second face, and at least four reinforcing assemblies that are embedded and mechanically retained in a prescribed location within the concrete member by their base and by the opposed faces of the concrete member. Each of the four reinforcing assemblies of the reinforced concrete structure comprises a support base and multiple hairpin-shaped rebar elements secured to the support base.

BRIEF DESCRIPTION OF THE DRAWINGS

A clear understanding of the key features of the invention summarized above may be had by reference to the appended drawings, which illustrate the system of the invention, although it will be understood that such drawings depict preferred embodiments of the invention and, therefore, are not to be construed as limiting its scope with regard to other embodiments which the invention intends and is capable of contemplating.

Accordingly, FIG. 1 represents a cross-sectional view of a concrete slab structure at the area surrounding the intersection of the slab structure with a supporting column, and showing undesirable cracking caused by punching shear forces.

FIG. 2 is a top view of the concrete slab structure depicted in FIG. 1.

FIG. 3 is a schematic diagram of a preferred embodiment of the reinforcing assembly system of the invention, and also shows several shapes that may be used for the hairpin-shaped rebar elements of the reinforcing assembly.

FIG. 4 is a schematic diagram of another preferred embodiment of the invention, illustrating one manner in which four reinforcing assembly systems may be used to provide reinforcement to a critical area surrounding the intersection of a slab and a supporting column.

FIG. 5 is a cross-sectional plan view of a reinforcing arrangement that uses eight of the reinforcing assembly system depicted in FIG. 3, showing the immediate vicinity of the intersection of a post-tensioned slab and a supporting column.

FIG. 6 is a sectional view of a specific section identified in FIG. 5, showing details of the reinforcing arrangement depicted therein.

FIG. 7 is a graph depicting and comparing load deflection relationship test results obtained by means of the reinforcing assembly system of the present invention.

FIG. 8 is a graph depicting and comparing load deflection relationship test results obtained by means of a reinforcing assembly system used in the prior art.

DETAILED DESCRIPTION OF THE INVENTION

The invention will now be described with reference to its application to a post-tensioned slab structure that is supported by a column, which may be a steel supporting column or a concrete supporting column. FIG. 1 represents a cross-sectional view of a concrete slab structure 101 at the “loaded” area 102 (also referred to as the “reaction” area) surrounding the intersection of the slab structure with concrete supporting column 103, and showing undesirable cracking 104 caused by punching shear forces. This is a typical two-way shear situation. FIG. 2 is a top view of the concrete slab structure depicted in FIG. 1 and shows post-tensioned concrete slab 201 (slab 101 in FIG. 1) intersected by concrete supporting column 203 (column 103 in FIG. 1) and creating loaded, or reaction, area 202 delineated by shear critical section perimeter 204. The maximum distance 205 at which the American Concrete Institute (“ACI”) requires any reinforcing assembly to be located inside a concrete slab supported by a column is usually expressed as “d/2”, with “d∞ being the effective depth of the slab, that is, the distance from the extreme compression fiber to the centroid of longitudinal tension reinforcement. This distance is shown in FIG. 2 as distance 205 from outer face 206 of support column 203 to the shear critical section perimeter 204.

FIG. 3 shows a schematic diagram of a preferred embodiment of this invention illustrating one manner in which the reinforcing assembly system of the invention may be designed to provide reinforcement to a critical area of interconnection between a slab and a cross member concrete structure such as a support column. The reinforcing assembly system of this invention is sometimes referred to as the “PTE Strand punching shear reinforcement”, or simply the “PTE-PSR”. The system involves a support base, comprising two elongate rebar members, or reinforcement bars, disposed substantially parallel to each other, and several hairpin-shaped shear-resisting rebar elements that are attached to the base. As shown in FIG. 3, base 301 comprises first elongate rebar member 302 and second elongate rebar member 303 disposed parallel to each other. Elongate rebar members 302 and 303 (sometimes referred to as “anchorage bars” or “rail bars”) are made of steel, but they may also be made of some other metal or hard material. The cross-sectional area of rebar members 302 and 303 is round, but it may also be rectangular or some other form. The length and thickness of rebar members 302 and 303 may vary with the specifications of the concrete structure for which they are designed. In the case of a standard flat slab, for example, they typically may be anywhere from about 1 to 5 feet long and from about ⅜ to ¾ inch in diameter (if round), and ¼ to ¾ inch in thickness (if square), depending on the applied loads and the effective depth of the slab. Also by way of illustration, if rectangular, the thickness of the rebar members may be anywhere between about ½ and 2 inches by between about ⅛ and ⅜ inch in cross-sectional area. Shear-resisting rebar elements 304-309 have a hairpin shape and are welded to base 301 at each of their ends, e.g., shear-resisting rebar element 309 is welded to rebar member 302 at end 310 and to rebar member 303 at end 311, while shear-resisting rebar element 308 is welded to rebar member 302 at end 312 and to rebar member 303 at end 313, and so on. The cross-sectional areas of shear-resisting rebar elements 304-309 may be substantially round or rectangular. The PTE-PSR reinforcing assembly depicted in FIG. 3 has six hairpin-shaped rebar elements, but it will be understood that more or less rebar elements may be used depending on the dimensions and other specifications of the concrete structure. Hairpin-shaped rebar elements 304-309 are made of steel, but they may also be made of some other metal or hard material. The length and the thickness of hairpin-shaped rebar elements 304-309 may vary with the specifications of the concrete structure for which they are designed. In the case of a standard 8-inch-thick flat slab, for example, they may be about 15 inches long (from end to end) and from about ¼ to ⅝ inches thick, depending on the applied loads and the effective depth of the slab. The hairpin-shaped rebar elements are sometimes referred to herein as “hairpins”. Various alternative shapes, e.g., shapes 314-319, of hairpin-shaped rebar elements 304-309 may be used, but the shapes should be substantially symmetrical, that is, the length of the legs, such as vertical legs 320 and 321 in the illustration of FIG. 3, should be essentially the same. Likewise, for any given assembly, the height of each hairpin, that is, the distance from its highest vertical point to the base of the assembly, should also be constant. In the illustration of FIG. 3 the height of each hairpin attached to base 301 is 4 inches, and the distance between the two legs of each hairpin is 2 inches, while the length of base 301 is 1^(1/2) feet. Rebar members 302 and 303 and hairpin-shaped rebar elements 304-309 may be made of steel reinforcing bars having the same thickness, or they may be made of other metals and have different thicknesses. In the illustration of FIG. 3, rebar members 302 and 303 and hairpin-shaped rebar elements 304-309 are made of ⅜-inch-diameter round steel. The elongate rebar members may be cast or cut to size, while the hairpin-shaped rebar elements may be shaped by bending, by hand or by special equipment, or they may be preformed by casting to the desired shapes and sizes. The elongate rebar members and the hairpin-shaped rebar elements may have a smooth surface, when cost savings constitute an important consideration, or they may be ribbed or corrugated in order to improve cohesion between the steel and the concrete, thereby providing better anchorage.

In using the reinforcing assembly system of the invention it is often best to place several, e.g., four, of these assemblies, or “PTE-PSRs”, right next to the loaded or reaction area, arranged in the manner depicted in FIG. 4, which is a schematic diagram illustrating one manner in which the assembly system of the invention may be used to provide reinforcement to a shear critical area surrounding the intersection of a post-tensioned slab and a concrete supporting column. Thus assemblies 401, 402, 403 and 404 are placed in cross-like fashion around loaded or reaction area 405 within critical section 406 that may occur, surrounding said intersection on the same plane, each disposed at an approximately right angle with the other.

FIG. 5 is a top cross-sectional view of a reinforcing arrangement using eight PTE-PSR reinforcing assemblies, showing the immediate vicinity of the intersection of a post-tensioned slab and a concrete supporting column. As stated above, the maximum distance at which the American Concrete Institute requires any reinforcing assembly to be located inside a concrete slab supported by a column is usually expressed as “d/2”, with “d” being the effective depth of the slab, that is, the distance from the extreme compression fiber to the centroid of longitudinal tension reinforcement. This critical distance is shown in FIG. 5 as distance 501 from outer face 502 of supporting column 503 to the first hairpin 504 of PTE-PSR 505. PTE-PSR 505 has six hairpins and is similar to the PTE-PSR depicted in FIG. 3. The placement of PTE-PSR 505 is such that the location of first hairpin 504 is made to coincide with shear critical section perimeter 514 of loaded or reaction area 513. PTE-PSRs 506, 507, 508, 509, 510, 511 and 512 are similarly configured and similarly placed around supporting column 503 on the same spatial plane as PTE-PSR 505 in cross-like fashion as illustrated in FIG. 5. When configured in sets of two hairpin assemblies, as illustrated in FIG. 5, improved shear resistance capabilities are also obtained if the distance between each assembly in a set is maintained at 2 d or less, that is, if the distance between each assembly is made to be equal to or less than twice the effective depth of the slab or concrete member. Thus, in the illustration of FIG. 5, distance 515 between PTE-PSR 505 and PTE-PSR 506 is set at less than twice the effective depth d of the slab; distance 516 between PTE-PSR 507 and PTE-PSR 508 is also set at less than twice the effective depth d of the slab; distance 517 between PTE-PSR 509 and PTE-PSR 510 is also set at less than 2 d; and distance 518 between PTE-PSR 511 and PTE-PSR 512 is likewise set at less than 2 d.

FIG. 6 is a front sectional view of Section A-A′ identified in FIG. 5 and showing frontal views of PTE-PSRs 505 and 510 (identified in FIG. 6 as PTE-PSRs 605 and 610) and showing the locations of PTE-PSRs 511 and 512 of FIG. 5 (identified in FIG. 6 as PTE-PSRs 611 and 612), all embedded within shear critical section perimeter 603 of loaded or reaction area 606 surrounding supporting column 602 in post-tensioned slab 601. First hairpin 604 of PTE-PSR 605 is located at distance 613 from supporting column face 607. First hairpin 604 of PTE-PSR 605 is also spaced from adjacent hairpin 608 of PTE-PSR 605 at a distance which is the same as distance 613; adjacent hairpin 608 is spaced from further adjacent hairpin 609 at a distance which is the same as distance 613, and so on. Likewise, first hairpin 614 of PTE-PSR 610 is located at distance 615 from supporting column face 616 which is the same as distance 613 between hairpin 604 and column face 607; while adjacent second hairpin 617 of PTE-PSR 610 is spaced from hairpin 614 at a distance which is the same as distance 615; and adjacent third hairpin 618 is separated from hairpin 617 at a distance which is the same as distance 615, and so on. In the illustration of FIG. 6, as well as in the illustration of FIG. 5, the slab effective depth (“d”) is 8 inches, and critical distances 501, 613 and 615 are 4 inches each.

Following is a detailed description of tests conducted in order to confirm the efficiency of the present invention and compare it with prior art techniques for reinforcing concrete members. FIG. 7 is a graph depicting and comparing load deflection relationship test results obtained by means of the reinforcing assembly system of the present invention (PTE-PSRs), as discussed below, while FIG. 8 is a graph depicting and comparing load deflection relationship test results obtained by means of a reinforcing assembly system used in the prior art (studrails), also discussed below. The specifications of the compared reinforcing assembly systems and the test parameters are shown in Table 1 below. The PTE-PSRs were made from reformed rebars (as shown in FIG. 3) PTE-PSRs were tested and compared using the same spacing and strength criteria as studrails. An important goal of these tests was to conduct an experimental investigation of the punching shear behavior of post-tensioned slabs (“PT slabs”) with hairpin assembly reinforcements. The slabs were designed to ensure punching shear failure and the tests were conducted by applying a central concentrated load on post-tensioned slabs. The test results obtained by using hairpin assembly reinforcements were compared to results obtained by using headed-stud reinforcements, also known as “headed-studs” or “studrails”, which had been previously used to increase punching shear capacity in flat slabs. The punching shear failure of the PT slabs was ensured by the following approach: The dimensions and thickness of the slab were chosen to yield a nominal punching shear stress of about 25 tons using the ACI equation for headed studs (8√{square root over (f′_(c))} at d/2 distance from the column face) which was about 40% of the capacity of the loading jack used for the tests. The slab was then analyzed using the so-called “Adapt floor-pro program”. The tests were conducted at the facilities of P.T.E. Strand Co., Inc., in Florida, which also provided materials and assistance in casting, stressing the tendons and conducting the tests. The maximum compressive stress in the concrete at the critical sections were below 75% of the concrete compressive strength, which would ensure a punching shear failure mode of the post-tensioned slab. The numbers and the profiles of the prestressing cables were then determined using the Adapt floor-pro program. Four post-tensioned concrete slabs with the same dimensions and post-tensioning were tested. Tests conducted with the hairpin assembly reinforcements (the PTE-PSRs) were designated PT-1 and PT-2, while tests conducted with the headed-stud reinforcements (the studrails) were designated PT-3 and PT-4. The specifications and parameters of the reinforcements are shown in Table 1. The test specimens were 6′-0″(1.83 m)×6′-0″(1.83 m)×4″(102 mm). The shear reinforcements of both specimens were located in the central region of the slab, around the loaded or reaction area. The concrete used for the slabs had a design strength of 3,500 psi (23.3 Mpa) and was supplied by a local ready-mix plant. The coarse aggregate used was #16 crushed limestone, and the water-cement ratio was 0.42. All specimens were cast from the same batch. Five standard cylinders of 6 in. (152.5 mm) radius×12 in. (305 mm) height were cast from each batch and kept in the same environment as the slab. The compressive strength after 7 days was 2,710 psi (18.7 Mpa) and the strength at the time of testing was 4,350 psi (30 Mpa).

The prestressing strands used were 0.5 in. (12.7 mm) in diameter, seven wire strands conforming to ASTM standard A421, with a specified ultimate strength of 270 ksi (1861 Mpa). The tendons were protected with a plastic sheathing to prevent the “cable-concrete” bond and to reduce friction at the time of stressing. #3 bars (10 mm) were used for fabricating hairpin assembly reinforcements conforming ASTM standard A421, with a specified yielding strength of 60 ksi (413.5 Mpa). The edge forms for the slabs were constructed using ¾ in. (19 mm) thick and 4 in. (102 mm) high plywood which were braced using 2 in. (51 mm)×6 in. (153 mm) wood studs. The edge forms were carefully aligned, leveled and nailed to the floor to help prevent movement during casting. The slabs were cast on the floor over plastic sheets. Prior to casting the slabs, the plastic sheets were oiled for ease of removal of the specimens. Chairs were used to ensure that the desired tendon profile was attained. Ready-mix concrete was delivered and pumped to the location of the specimens. The concrete was vibrated and the final slab finish achieved using steel trowels and wooden floats. A plastic cover was placed over the slabs for a 15-day curing period.

The specimens were tested in an elevated position using a steel test frame. Application of an upward load allowed for the observation of the punching shear failure on the top surface of the slab. The reaction frame was designed and fabricated of structural steel. The central loading was applied upwards and the concrete slab was held down at four locations which were 3 ft. (915 mm) apart. The slab also had a 1.5 ft. (457 mm) overhang on each side. The tendons were stressed up to 33 kips (146.5 KN) after the slab was positioned on the test frame. The loading was accomplished by using a hydraulic jack. The hydraulic jack was previously calibrated to yield the applied load. A dial gauge was mounted at the center of the slab to measure the displacement of the slab. Load cells were also placed between the edge of the slab and the anchoring mechanism of the prestressing tendons to measure the force in the four central tendons. The strain-gage based load cells were manufactured by Honeywell Sensotec and had a capacity of 50 kips (222 KN) each. These load cells were connected to a 4-channel digital indicator which displayed the tendon force.

The tests were carried out by increasing the pressure in the hydraulic jack and recording the central deflection and the tendon forces at each increment of the load. The data for one of the slabs with hairpin assembly reinforcements (PT-1) are provided in Table 2. The first crack in PT-1 was observed at a load of 30.5 kips (135.7 KN). The second perpendicular crack in PT-1 appeared at a load of 43.2 kips (192.2 KN) in PT-1. The maximum load carried by PT-1 was 63.8 kips (283.7 KN). Both specimens PT-1 and PT-2 failed in the flexural mode. The results presented in Table 2 indicate that the tendon force increases linearly with the load up to the point of failure. The maximum stress in the tendon at failure was 190 ksi (1308 Mpa). The use of the hairpin assembly reinforcements (the PTE-PSRs) caused flexural failure to occur before punching shear failure in both specimens PT-1 and PT-2. The central load vs. deflection plots for PT-1 and PT-2 are provided in FIG. 7. The load deflection behavior appears to be essentially bi-linear with the change in slope occurring close to the first visible crack.

The data obtained for one of the slabs with the studrails (PT-3) is provided in Table 3. The first crack in PT-3 was observed at a load of 30.5 kips (135.7 KN) and the second perpendicular crack appeared at a load of 39.9 kips (177.5 KN). The maximum load reached was 57.3 kips (255 KN). The central load vs. deflection plots for PT-3 and PT-4 are provided in FIG. 8. The load deflection behavior appears to be essentially bi-linear with the change in slope occurring close to the first visible crack. Both specimens PT-3 and PT-4 failed in punching shear mode. The shape of the failure surface was roughly square with a dimension of about 22 in. (559 mm) to 22 in. (559 mm) each side.

The ACI approach for punching shear capacity with headed-stud reinforcements is based on the nominal punching shear stress of a critical section located at a distance d/2 from the column face and the length of the shear reinforcement as described earlier. The test results are compared with the values obtained from the ACI provision of headed-stud reinforcements in Table 4. The ACI-421.1 R recommendation for nominal punching shear stress using headed-studs is 8√{square root over (f′_(c))} at a distance d/2 from the column face. For hairpin assembly reinforcements, or PTE-PSRs, (PT-1 & PT-2), the average punching shear strength was 62.2 Kips (276.7 KN) which is equal to a nominal punching shear stress of 10.2√{square root over (f′_(c))}. For PT slabs reinforced with headed-studs (PT-3 & PT-4), the ACI predictions were found to be almost equal or slightly conservative. The average capacity was 50.2 Kips (223.3 KN) which corresponds to a nominal shear stress of 8.2√{square root over (f′_(c))}. The results obtained for punching shear using the PTE-PSRs were about 20% higher than those obtained for punching shear using the headed-studs.

The tests demonstrated that the PT slabs with headed-stud reinforcements failed in punching shear, while PT slabs with hairpin assembly reinforcements (PTE-PSRs) failed in flexure. The test results with the headed-stud reinforcements were almost equal to those predicted by the ACI equation. The tests with hairpin assembly reinforcements had the shear failure prevented, and almost complete redistribution of bending moments were achieved prior to collapse. The PT slab capacity with hairpin assembly reinforcements were about 20% higher than the PT slab capacity with the headed-stud reinforcements. The nominal shear stress for a PT slab with hairpin assembly reinforcements was equal to 10.2√{square root over (f′_(c))} and could actually be higher as the slabs failed in flexure. The test results show that, in terms of shear reinforcement capability, concrete structures using hairpin assembly reinforcements in PT slabs provide superior confinement of the concrete where punching shear failures tend to occur and behave structurally better than concrete structures that use headed-stud reinforcements.

TABLE 1 Specifications and Parameters of Load Deflection Relationship Test Number of Number of Number of Studrail/ Studrail/ Studrail/ assembly rails/ studrails/ Assembly test hairpin hairpin hairpin elongated rebars hairpins per system specimens diameter height spacing per column assembly Studrails 2 ⅜ in 4 in 1.5 in 8 6 PTE-PSRs 2 ⅜ in 4 in 1.5 in 8 6

TABLE 2 Test results for PT-1 Tendon forces measured by Load Deflection load cells (Kips) (in) (lbs) Remarks 0.00 0.000 21111 22670 23217 25750 5.2 0.009 21110 22676 23223 25723 10.5 0.017 21152 22602 23237 25731 16.4 0.027 21204 22645 23259 25748 22.3 0.038 21269 22707 23288 25794 25.0 0.046 21306 22745 23317 25798 30.5 0.069 21387 22828 23422 25902 1st visible crack 36.6 0.116 21500 22924 23748 26230 43.2 0.199 21808 23135 24282 26772 2^(nd) visible crack 49.2 0.338 22500 23746 25067 27603 54.6 0.446 23167 24391 25736 27323 60.6 0.629 24114 25305 26545 29182 63.8 0.801 24562 25743 26848 19465 punching shear failure

TABLE 3 Test results for PT-3 Tendon forces measured Load Deflection by load cells (Kips) (in) (lbs) remarks 0.00 0.000 24188.0 21328.0 23519.0 17841.0 5.2 0.008 24191 21337 23528.0 17852 10.5 0.018 24196.0 21357 23588 17903 16.4 0.031 24218.0 21388 23640 17987 22.3 0.043 24241.0 21416 23738 18075 27.8 0.064 24305.0 21502 23888 18229 30.5 0.082 24421.0 21618 23970 18303 1st visible crack 36.6 0.154 24919.0 22156 24340 18675 39.9 0.203 25217.0 22493 24590 18941 2^(nd) visible crack 43.2 0.251 25544.0 22824 24841 19238 49.2 0.369 26270.0 23622 25496 20030 54.6 0.540 27147.0 24645 26329 21057 57.4 0.653 27660.0 25272 26857 21770 punching shear failure

TABLE 4 Comparison of punching shear test results with ACI provision Test results ACI Equation Shear Nominal shear Nominal shear Specimen Failure loads Average failure perimeter, b₀ stress. stress. designation Kips/KN load, Kips/KN in/mm psi/Mpa psi/Mpa PT-1 63.82/283.8 62.21/276.65 28.80/731.5 10.2{square root over (ƒ′_(c))}/0.85{square root over (ƒ′_(c))} N.A PT-2 60.60/269.5 PT-3 57.36/255.0 50.30/223.60 28.80/731.5 8.2{square root over (ƒ′_(c))}/0.68{square root over (ƒ′_(c))} 8{square root over (ƒ′_(c))}/0.66{square root over (ƒ′_(c))} PT-4 43.21/192.2 Conversion Factors and Notations: 1 in. = 25.4 mm; 1 kip = 4.448 N; 1 ksi = 6.895 Mpa A_(c) = area of critical section = b₀d b₀ = perimeter of critical shear section at a distance d/2 from the column face. d = distance from the extreme compression fiber to the centroid of tension reinforcement ƒ′_(c) = concrete compressive strength N.A = not applicable

The hairpin assembly reinforcements described herein may be set in the concrete structure by placing them in a light-weight plastic support base, such as a stool, or “chair”, and setting the support base and the hairpin assembly reinforcements on wood forms of the type commonly used commercially to set concrete and concrete reinforcements. Normally, the assembly can be secured to the support base by means of wires and the support based nailed or otherwise fastened to the wood forms before pouring the concrete. The techniques for embedding reinforcing devices in concrete are well known to those skilled in art of concrete pouring and handling, and any of a number of such techniques may be used for this purpose. The reinforcing assemblies of the present invention may also be placed in the post-tensioned anchorage zone of the reinforced concrete structure.

While the present invention has been described in terms of particular embodiments and applications, in both summarized and detailed forms, it is not intended that these descriptions in any way limit its scope to any such embodiments and applications, and it will be understood that many substitutions, changes and variations in the described embodiments, applications and details of the method and system illustrated herein and of their operation can be made by those skilled in the art without departing from the spirit of this invention. 

1. A reinforcing assembly for use in structural concrete members, comprising: (a) a base, comprising a first elongate rebar member and a second elongate rebar member, said first and second elongate rebar members disposed substantially parallel to each other; and (b) a plurality of shear-resisting rebar elements having two opposing ends and cast or reformed in a generally hairpin shape, said shear-resisting rebar elements disposed on a common plane in generally parallel orientation to each other and bridging said first and second elongate rebar members comprising said base, each said rebar element having its first opposing end secured to said first base elongate rebar member and its second opposing end secured to said second base elongate rebar member.
 2. The reinforcing assembly of claim 1, wherein said first and second elongate rebar members comprising said base and disposed substantially parallel to each other are spatially disposed on substantially the same plane with respect to each other.
 3. The reinforcing assembly of claim 1, wherein said generally hairpin-shaped rebar elements bridging said first and second elongate rebar members comprising said base have a substantially smooth surface.
 4. The reinforcing assembly of claim 1, wherein said generally hairpin-shaped rebar elements bridging said first and second elongate rebar members comprising said base are ribbed or corrugated.
 5. The reinforcing assembly of claim 1, wherein each said rebar element has its first opposing end welded to said first base elongate rebar member and its second opposing end welded to said second base elongate rebar member.
 6. The reinforcing assembly of claim 1, wherein all of said generally hairpin-shaped rebar elements bridging said first and second elongate rebar members are spaced at the same distance from each other on said base.
 7. The reinforcing assembly of claim 1, wherein the cross-sectional area of each of said generally hairpin-shaped rebar elements is substantially round.
 8. The reinforcing assembly of claim 1, wherein the shape and the height of each of said generally hairpin-shaped rebar elements are substantially the same.
 9. The reinforcing assembly of claim 1, wherein each of said generally hairpin-shaped rebar elements is made of steel.
 10. The reinforcing assembly of claim 1, wherein said first and second elongate rebar members and said generally hairpin-shaped rebar elements are made of round steel rebars having the same cross-sectional area and wherein all said generally hairpin-shaped rebar elements have the same shape and height.
 11. A reinforced concrete structure, comprising: (a) a concrete member having a first face and a generally opposed second face; and (b) at least four reinforcing assemblies embedded within said concrete structure at prescribed locations, each said reinforcing assembly comprising (i) a base, comprising a first elongate rebar member and a second elongate rebar member, said first and second elongate rebar members disposed substantially parallel to each other; and (ii) a plurality of shear-resisting rebar elements having two opposing ends and cast or reformed in a generally hairpin shape, said shear-resisting rebar elements spatially disposed on a common plane in generally parallel orientation to each other and bridging said first and second elongate rebar members comprising said base, each said rebar element having its first opposing end secured to said first base elongate rebar member and its second opposing end secured to said second base elongate rebar member, wherein each of said at least four reinforcing assemblies is retained at said prescribed locations by said base and said opposed concrete member faces.
 12. The reinforced concrete structure of claim 11, wherein said first and second elongate rebar members comprising said reinforcing assembly base and disposed substantially parallel to each other are spatially disposed on substantially the same plane with respect to each other.
 13. The reinforced concrete structure of claim 11, wherein said generally hairpin-shaped rebar elements bridging said first and second elongate rebar members comprising said base have a substantially smooth surface.
 14. The reinforced concrete structure of claim 11, wherein said generally hairpin-shaped rebar elements bridging said first and second elongate rebar members comprising said base are ribbed or corrugated.
 15. The reinforced concrete structure of claim 11, wherein each said rebar element has its first opposing end welded to said first base elongate rebar member and its second opposing end welded to said second base elongate rebar member.
 16. The reinforced concrete structure of claim 11, wherein all of said generally hairpin-shaped rebar elements bridging said first and second elongate rebar members are spaced at the same distance from each other on said base.
 17. The reinforced concrete structure of claim 11, wherein the cross-sectional area of each of said generally hairpin-shaped rebar elements of said reinforcing assemblies is substantially round.
 18. The reinforced concrete structure of claim 11, wherein the shape and the height of each of said generally hairpin-shaped rebar elements of said reinforcing assemblies are substantially the same.
 19. The reinforced concrete structure of claim 11, wherein four reinforcing assemblies are embedded within said concrete structure and arranged in cross-like fashion at substantially right angles with respect to each other on substantially the same plane and each of said generally hairpin-shaped rebar elements is made of steel.
 20. The reinforced concrete structure of claim 11, wherein said first and second elongate rebar members and said hairpin-shaped rebar elements of said reinforcing assemblies are made of round steel rebars having the same cross-sectional area, and wherein the shape and the height of each of said generally hairpin-shaped rebar elements of said reinforcing assemblies are substantially the same.
 21. A reinforced concrete structure, comprising: (a) a concrete member having a first face and a generally opposed second face; (b) a column supporting said concrete member; and (c) at least four reinforcing assemblies embedded within said concrete member at prescribed locations around said supporting column, each said reinforcing assembly comprising (i) a base, comprising a first elongate rebar member and a second elongate rebar member, said first and second elongate rebar members disposed substantially parallel to each other; and (ii) a plurality of rebar elements having two opposing ends and cast or reformed in a generally hairpin shape, said generally hairpin-shaped rebar elements spatially disposed on a common plane in generally parallel orientation to each other and bridging said first and second elongate rebar members comprising said base, each said generally hairpin-shaped rebar element having its first opposing end secured to said first base elongate rebar member and its second opposing end secured to said second base elongate rebar member, said at least four reinforcing assemblies placed within said concrete member in cross-like fashion at substantially right angles with respect to each other on substantially the same plane, and wherein each of said at least four reinforcing assemblies is mechanically retained at said prescribed locations by said base and by said opposed faces of said concrete member.
 22. The reinforced concrete structure of claim 21, wherein said first and second elongate rebar members comprising said reinforcing assembly base and disposed substantially parallel to each other are spatially disposed on substantially the same plane with respect to each other.
 23. The reinforced concrete structure of claim 21, wherein each of the said at least four reinforcing assemblies embedded within said concrete member in cross-like fashion is placed around said supporting column at a distance which is equal to or less than one-half of the effective depth of said concrete member.
 24. The reinforced concrete structure of claim 21, wherein four reinforcing assemblies are embedded within said concrete member.
 25. The reinforced concrete structure of claim 21, wherein eight reinforcing assemblies are embedded within said concrete member.
 26. The reinforced concrete structure of claim 21, wherein the shape and the height of each of said generally hairpin-shaped rebar elements of said reinforcing assemblies are substantially the same.
 27. The reinforced concrete structure of claim 21, wherein four reinforcing assemblies are embedded within said concrete structure and arranged in cross-like fashion at substantially right angles with respect to each other on substantially the same plane and each of said generally hairpin-shaped rebar elements is made of steel.
 28. The reinforced concrete structure of claim 21, wherein eight reinforcing assemblies are embedded within said concrete structure and arranged in cross-like fashion at substantially right angles with respect to each other on substantially the same plane and each of said generally hairpin-shaped rebar elements is made of steel.
 29. The reinforced concrete structure of claim 21, wherein said first and second elongate rebar members and said hairpin-shaped rebar elements of said reinforcing assemblies are made of round steel rebars having the same cross-sectional area, and wherein the shape and the height of each of said generally hairpin-shaped rebar elements of said reinforcing assemblies are substantially the same.
 30. The reinforced concrete structure of claim 21, wherein said supporting column is made of concrete.
 31. The reinforced concrete structure of claim 21, wherein said supporting column is made of steel. 